explain how to estimate order of magnitudes
Answers
An order of magnitude is an exponential change of plus-or-minus 1 in the value of a quantity or unit. The term is generally used in conjunction with power-of-10 scientific notation. In base 10, the most common numeration scheme worldwide, an increase of one order of magnitude is the same as multiplying a quantity by 10. An increase of two orders of magnitude is the equivalent of multiplying by 100, or 102. In general, an increase of n orders of magnitude is the equivalent of multiplying a quantity by 10n. Thus, 2315 is one order of magnitude larger than 231.5, which in turn is is one order of magnitude larger than 23.15. As values get smaller, a decrease of one order of magnitude is the same as multiplying a quantity by 0.1. A decrease of two orders of magnitude is the equivalent of multiplying by 0.01, or 10-2. In general, a decrease of n orders of magnitude is the equivalent of multiplying a quantity by 10-n. Thus, 23.15 is one order of magnitude smaller than 231.5, which in turn is one order of magnitude smaller than 2315.